<s>
In	O
mathematical	O
physics	O
,	O
constructive	B-Algorithm
quantum	I-Algorithm
field	I-Algorithm
theory	I-Algorithm
is	O
the	O
field	O
devoted	O
to	O
showing	O
that	O
quantum	O
field	O
theory	O
can	O
be	O
defined	O
in	O
terms	O
of	O
precise	O
mathematical	O
structures	O
.	O
</s>
<s>
Attempts	O
to	O
put	O
quantum	O
field	O
theory	O
on	O
a	O
basis	O
of	O
completely	O
defined	O
concepts	O
have	O
involved	O
most	O
branches	O
of	O
mathematics	O
,	O
including	O
functional	B-Application
analysis	I-Application
,	O
differential	O
equations	O
,	O
probability	O
theory	O
,	O
representation	O
theory	O
,	O
geometry	O
,	O
and	O
topology	B-Architecture
.	O
</s>
<s>
One	O
discovery	O
of	O
the	O
theory	O
that	O
can	O
be	O
related	O
in	O
non-technical	O
terms	O
,	O
is	O
that	O
the	O
dimension	O
d	O
of	O
the	O
spacetime	B-Protocol
involved	O
is	O
crucial	O
.	O
</s>
<s>
The	O
traditional	O
basis	O
of	O
constructive	B-Algorithm
quantum	I-Algorithm
field	I-Algorithm
theory	I-Algorithm
is	O
the	O
set	O
of	O
Wightman	O
axioms	O
.	O
</s>
